You really need to go to the source - send in your paper work to ASL and send an email to the CAA telling them what you want to do...no offence to the very helpful replies but if you are making a big decision like this you need to get it right.
https://www.caa.govt.nz/about_caa/co..._infr_pers.htm
The flight test is a little probmatic in so much you need to be type rated on the aircraft.
AirNZ can do the flight test as can a few other operators - one other option is in a KingAir and there is a Mojave that might be available. Some operators let you hire these types for flight tests but it seems to be on an individual basis.
Have a good look at the Fit & Proper Person requirement - you will probably have to get some documents in the States before you leave to cover that.
It will not be a cheap process.